Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

A wave mechanism for the anomalous acceleration without dark energy

Blake Temple

University of California-Davis

I present joint work with Joel Smoller and Zeke Vogler in which we describe a simple-wave mechanism capable of inducing an anomalous acceleration into the galaxies without the need for Dark Energy. Our theory is based on authors' identification of a one parameter family of self-similar waves that perturb the critical Friedmann spacetime during the radiation epoch of the Big Bang. The critical Friedmann spacetime is the basis for the Standard Model of Cosmology (SM), but Dark Energy in the form of the Cosmological Constant has been incorporated into Einstein's theory as the only way to make the uniform Friedmann spacetime consistent with accelerations implied by the Nobel Prize winning supernova data of 1999. Dark Energy is interpreted as an anti-gravitating, constant in time vacuum energy density, but is otherwise unknown. To work it must account for some seventy percent of the energy density of the universe at present time. Our alternative theory explores the hypothesis that a center of fluctuation from the critical Friedmann universe without Dark Energy, would decay to one of our identified self-similar waves by the end of the radiation epoch. This is a plausible assumption in part because the Glimm-Lax mechanisms for decay to simple-wave patterns are in place during the radiation epoch of the Big Bang. Since introducing this idea, authors' program has concentrated on bringing the corrections to the SM, induced by this family of waves at the end of radiation, up to present time, so that the predictions could be compared with Dark Energy. We now have the answer, and it is surprisingly compelling. The punch line is that the SM critical Friedmann spacetime is {it unstable} to perturbation by this family of waves, and under small perturbation, the quadratic corrections at the center of the wave tend toward a new Stable Rest Point. The evolution away from the SM and toward this Stable Rest Point then induces an {it increasing} quadratic correction to redshift vs luminosity at the center of the wave, the center becomes more and more uniform in density further and further out, and the increasing expansion rate near the center passes through the {it same values} and tends to {it the same limit} as Dark Energy--i.e., the {it same range} of accelerations are produced by the Wave Theory during evolution toward the Stable Rest Point, as are produced by Dark Energy as its fraction with Matter increases from zero to one. The third order correction term implies a slightly larger anomalous acceleration far from the center in the Wave Theory, and this makes for a verifiable prediction. We view this as the simplest mechanism that can account for the anomalous acceleration of galaxies within Einstein's original theory without the need for Dark Energy, and as such, provides a baseline model to which all other theories of the anomalous acceleration can be compared.